Modal Kinematic Analysis of a Parallel Kinematic Robot with Low-Stiffness Transmissions

Several industrial robotic applications that require high speed or high stiffness-to-inertia ratios use parallel kinematic robots. In the cases where the critical point of the application is the speed, the compliance of the main mechanical transmissions placed between the actuators and the parallel kinematic structure can be significantly higher than that of the parallel kinematic structure itself. This paper deals with this kind of system, where the overall performance depends on the maximum speed and on the dynamic behavior. Our research proposes a new approach for the investigation of the modes of vibration of the end-effector placed on the robot structure for a system where the transmission’s compliance is not negligible in relation to the flexibility of the parallel kinematic structure. The approach considers the kinematic and dynamic coupling due to the parallel kinematic structure, the system’s mass distribution and the transmission’s stiffness. In the literature, several papers deal with the dynamic vibration analysis of parallel robots. Some of these also consider the transmissions between the motors and the actuated joints. However, these works mainly deal with the modal analysis of the robot’s mechanical structure or the displacement analysis of the transmission’s effects on the positioning error of the end-effector. The discussion of the proposed approach takes into consideration a linear delta robot. The results show that the system’s natural frequencies and the directions of the end-effector’s modal displacements strongly depend on its position in the working space.

A novel, low-cost technique for modelless calibration of a 3-axis parallel kinematic machine

Purpose The purpose of this paper is to propose a novel measurement technique and a modelless calibration method for improving the positioning accuracy of a three-axis parallel kinematic machine (PKM). The aim is to present a low-cost calibration alternative, for small and medium-sized enterprises, as well as educational and research teams, with no expensive measuring devices at their disposal. Design/methodology/approach Using a chessboard pattern on a ground-truth plane, a digital indicator, a two-dimensional eye-in-hand camera and a laser pointer, positioning errors are explored in the machine workspace. With the help of these measurements, interpolation functions are set up per direction, resulting in an interpolation vector function to compensate the volumetric errors in the workspace. Findings Based on the proof-of-concept system for the linear-delta PKM, it is shown that using the proposed measurement technique and modelless calibration method, positioning accuracy is significantly improved using simple setups. Originality/value In the proposed method, a combination of low-cost devices is applied to improve the three-dimensional positioning accuracy of a PKM. By using the presented tools, the parametric kinematic model is not required; furthermore, the calibration setup is simple, there is no need for hand–eye calibration and special fixturing in the machine workspace.

Extended PKM Fixturing System for Micro-Positioning and Vibration Rejection in Machining Application

The paper aims to present a mechatronic device able to micro-position the workpiece and to reject disturbances due to machining operation. A decoupling method is proposed for a parallel kinematic machine (PKM) fixturing platform composed by a 3-DoF flexure-based piezo-actuated mechanism. The parallel platform, with a vertical motion and two rotations, is described and its kinematics and dynamics are studied. The coupling undesirable effect is investigated based on a set of poses. To improve the quasi-static regulator model for a set-point following system, a bump less switching controller and a fine-tuning procedure, to estimate the parameter uncertainty and enable the external disturbance containment in an extended broadband frequency range, are presented. The platform and the piezo-actuator controllers are modelled based on a gain scheduling, standard ISA form method, to guarantee the stability. The accuracy is demonstrated through a set of simulations and experimental comparisons. A sensitivity analysis that evaluates the tracking performance and the disturbance rejection based on the number of signal amplitudes, frequencies, and phases is discussed. A validation phase has shown that the developed architecture presents a steady state error lower than 1.2 µm, a vibration reduction of 96% at 1130 Hz with a maximum resolving time of 6.60 ms.

Method for assessing the current and additional load on the parallel kinematic structure mechanisms electric drive system

Introduction. The problem of the load on an electric drive system in a parallel kinematic structure is considered. The task of developing a fault-tolerant system that provides performing a given process in case of a failure of one or more drives is described. The work objective is to create a method for estimating the current and additional load on each drive of the mechanism of a parallel kinematic structure. The solution enables to correct the operating mode when performing a given process without compromising serviceable drives.Materials and Methods. Previously, a diagnostic method was developed. It is based on the calculation and analysis of the coefficients of straight lines that approximate the envelopes of the values of the wavelet transform coefficients of electric motor current signals, taking into account the characteristic scales. This makes it possible to determine the current technical condition of the electric motor and find malfunctions. The logical continuation of this approach is the proposed method for assessing the current and additional load. It provides finding the current load on the drive based on the coefficients of the lines approximating the envelopes of the wavelet coefficients of the current signal. To calculate the additional load, the number and location of faulty drives are taken into account.Results. For each scale of the wavelet coefficients, the relative coefficients and the current load on each drive are determined. The possibility of redistributing the load to two adjacent jacks was checked; the behavior of the system in this case was investigated. The load moved by the faulty jack is redistributed to two adjacent jacks in equal shares — 14.76 % each. The total load on the drives is 44.28 %, which is safe for the servo. The load on the drive of the fourth jack does not change (29.52 %). The drives have a sufficient safety margin. It is established that all three operating modes are acceptable for the studied servo drive, and they do not cause dynamic overloads and premature failure.Discussion and Conclusions. The experimental studies on the method of assessing the current and additional load have shown its adequacy and high efficiency. It was found that when the drives were disconnected from one of the racks of the mechanism, the system performed a load redistribution on the drives. Thus, it was possible to avoid their dynamic overloads and premature failure. This means that the solution is able to ensure the reliable functioning of the complex at the time of renovation work.

Design and simulation of a PK testbed for head impact evaluation

This paper presents the design and simulation of a Parallel Kinematic (PK) testbed for head impacts. The proposed design is presented as a novel head impact testbed using a parallel platform as main motion simulation mechanism. The testbed is used to give a motion to a head mannequin to impact against a steel plate. In addition, the platform in the testbed allows to modify the orientation of the head mannequin model to evaluate different types of impacts. The testbed has been modeled with software MS ADAMS® to evaluate its performance with a dynamic simulation and to characterize the testbed design during top and lateral impact events. Results show that PK testbed gives a significant force and acceleration to the head mannequin at the moment of the impact.

On the Structural Constraint and Motion of 3-PRS Parallel Kinematic Machines

This paper presents a consistent analytic kinematic formulation of the 3-PRS parallel manipulator (PM) with a parasitic motion by embedding the velocity level structural constraint equation into the motion expression. Inverse rate kinematics (IRK) is solved with a simple constraint compatible velocity profile, which is obtained by projecting the instantaneous restriction space onto the motion space. Moreover, the systematic method to reveal the parasitic motion is introduced. Thus, the parasitic terms are automatically identified from the main motions. Unlike the usual approach, this study does not consider any explicit parasitic motion expression. Consequently, the derivation of constraint compatible input velocity, which comprises the parasitic term, is simplified. To incorporate the parasitic motion into the task velocity, constraint Jacobian of the manipulator is analytically obtained first. The manipulator Jacobian is extended to incorporate the passive joint’s information apart from the active joints and structural constraint. Hence, the dimension of the Jacobian matrix used to solve IRK is 9 × 6. The validity of the IRK is proved by the Bordered Gramian based forward rate kinematics (FRK). Then, an accurate numerical integration, RK4, is applied to the joint velocity of IRK to obtain the manipulator’s joint values. Consequently, the moving plate’s pose is obtained via forward position kinematics computed using integrated active and passive joint values for validation. The projection matrix used to get compatible constraint motion adjusts our input velocity and makes it compatible with the structural constraint policy, and the parasitic motion is embedded easily. Thus, an explicit formulation of the parasitic motion equation is not required, as the usual practice. Finally, the study presented numerical simulations to show the validity of the outlined resolutions. This paper’s result and analysis can be uniformly applied to other parallel manipulators with less than 6 DoFs.

Calibration of Parallel Kinematic Machine Based on Stewart Platform – A Literature Review

Stewart platform-based Parallel Kinematic Machines (PKM) have been extensively studied by researchers due to their inherent finer control characteristics. This has opened its potential deployment opportunities in versatile critical applications like the medical field, engineering machines, space research, electronic chip manufacturing, automobile manufacturing, etc. All these precise, complicated, and repeatable motion applications require micro and nano-scale movement control in 3D space; a 6-DOF PKM can take this challenge smartly. For this, the PKM must be more accurate than the desired application accuracy level and thus proper calibration for a PKM robot is essential. Forward kinematics-based calibration for such hexapod machines becomes unnecessarily complex and inverse kinematics complete this task with much ease. To analyze different techniques, an external instrument-based, constraint-based, and auto or self-calibration-based approaches have been used for calibration. This survey has been done by reviewing these key methodologies, their outcome, and important points related to inverse kinematic-based PKM calibrations in general. It is observed in this study that the researchers focused on improving the accuracy of the platform position and orientation considering the errors contributed by a single source or multiple sources. The error sources considered are mainly structural, in some cases, environmental factors are also considered, however, these calibrations are done under no-load conditions. This study aims to understand the current state of the art in this field and to expand the scope for other researchers in further exploration in a specific area.